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In the World Cup of soccer, 32 teams compete for the title. What is the number of ways that the winner, runner-up, and third place prizes could be awarded?

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Introductory Statistics
OER Edition, 2013
Openstax
ISBN: 9781938168208

Related questions

2 (a) Suppose you start with one Red and one Black ball in a bag. You draw a ball at random from the bag repeatedly and look at its colour each time. After each successive draw, you double the number of Red balls and triple the number of Black balls in the bag before the next draw (eg. on the third draw there will be 4 Red and 9 Black balls in the bag). Explain why you will draw only finitely many Red balls in total with probability 1. [3 marks]

(b) In a modified game, suppose instead that for before the nth draw, you first make an n by n square arrangement of balls where the perimeter balls are all Red and any interior balls are Black ball. Thus, on the second draw there are 4 Red and 0 Black in the bag (22 in total), on the third draw there are 8 Red and 1 Black in the bag (32 in total), on the fourth there are 12 Red and 4 Black in the bag (42 in total), and so on. How many Red and Black balls will there be on the nth draw? Will you still draw only finitely many red balls? Explain your answer. [4 marks]

People enter a restaurant and check their hat at the coat check, but since the worker is new, he makes the mistake of throwing all the hats in a pile. When the patrons return to claim their hats at the end of the evening, the worker gives each person a random hat from the pile.Ā Ā 

1. What is the probability that no one receives their own hat back if there are only 2guests?

2. What is the probability that no one receives their own hat back if there are 3 guests?

3. What is the probability that no one receives their own hat back if there are 4 guests?

4. What is the probability that no one receives their own hat back if there are 8 guests?

5.What is the probability that no one receives their own hat back if there are 10 guests?

To solve, build a systematic method. For example, one way you could do it is by defining several events, where P_i = the number of ways of a person i to recive their hat correctly, and then the number of ways that at least one person to recive their hat is the union of P_1,...,P_n; finally, you can count this using inclusion/exlusion, then count the complement to finish the problem.Ā 

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The table shows data collected on the relationship between the average daily temperature and coffee sales (in hundreds of dollars) at a coffee shop. The line of best fit for the data is yĢ‚ =āˆ’0.68x+85.1. Assume the line of best fit is significant and there is a strong linear relationship between the variables.

According to the line of best fit, what would be the predicted number of coffee sales (in hundreds of dollars) for an average daily temperature of 32 degrees? Round your answer to two decimal places, as needed.

Temperature (Degrees) Coffee Sales (in hundreds of dollars)
30 65
40 58
50 50
60 45

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